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Mirrors > Home > ILE Home > Th. List > eqtr2d | Unicode version |
Description: An equality transitivity deduction. (Contributed by NM, 18-Oct-1999.) |
Ref | Expression |
---|---|
eqtr2d.1 | |
eqtr2d.2 |
Ref | Expression |
---|---|
eqtr2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr2d.1 | . . 3 | |
2 | eqtr2d.2 | . . 3 | |
3 | 1, 2 | eqtrd 2150 | . 2 |
4 | 3 | eqcomd 2123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-4 1472 ax-17 1491 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 |
This theorem is referenced by: 3eqtrrd 2155 3eqtr2rd 2157 ifandc 3478 onsucmin 4393 elxp4 4996 elxp5 4997 csbopeq1a 6054 ecinxp 6472 fundmen 6668 fidifsnen 6732 sbthlemi3 6815 ctm 6962 addpinq1 7240 1idsr 7544 prsradd 7562 cnegexlem3 7907 cnegex 7908 submul2 8129 mulsubfacd 8148 divadddivap 8455 infrenegsupex 9357 xadd4d 9636 fzval3 9949 fzoshftral 9983 ceiqm1l 10052 flqdiv 10062 flqmod 10079 intqfrac 10080 modqcyc2 10101 modqdi 10133 frecuzrdgtcl 10153 frecuzrdgfunlem 10160 seq3id2 10250 expnegzap 10295 binom2sub 10373 binom3 10377 fihashssdif 10532 reim 10592 mulreap 10604 addcj 10631 resqrexlemcalc1 10754 absimle 10824 infxrnegsupex 11000 clim2ser 11074 serf0 11089 summodclem3 11117 mptfzshft 11179 fsumrev 11180 fsum2mul 11190 isumsplit 11228 cvgratz 11269 mertenslemi1 11272 ef4p 11327 tanval3ap 11348 efival 11366 sinmul 11378 divalglemnn 11542 dfgcd2 11629 lcmgcdlem 11685 lcm1 11689 oddpwdclemxy 11774 oddpwdclemdc 11778 hashgcdeq 11831 ennnfonelemp1 11846 strslfvd 11927 cnclima 12319 dveflem 12782 tangtx 12846 abssinper 12854 |
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